(u^3-8)-3u+8=0

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Solution for (u^3-8)-3u+8=0 equation:

Simplifying
(u3 + -8) + -3u + 8 = 0

Reorder the terms:
(-8 + u3) + -3u + 8 = 0

Remove parenthesis around (-8 + u3)
-8 + u3 + -3u + 8 = 0

Reorder the terms:
-8 + 8 + -3u + u3 = 0

Combine like terms: -8 + 8 = 0
0 + -3u + u3 = 0
-3u + u3 = 0

Solving
-3u + u3 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), 'u'.
u(-3 + u2) = 0

Subproblem 1Set the factor 'u' equal to zero and attempt to solve:

Simplifying
u = 0

Solving
u = 0

Move all terms containing u to the left, all other terms to the right.

Simplifying
u = 0
Subproblem 2Set the factor '(-3 + u2)' equal to zero and attempt to solve:

Simplifying
-3 + u2 = 0

Solving
-3 + u2 = 0

Move all terms containing u to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + u2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + u2 = 0 + 3
u2 = 0 + 3

Combine like terms: 0 + 3 = 3
u2 = 3

Simplifying
u2 = 3

Take the square root of each side:
u = {-1.732050808, 1.732050808}Solutionu = {0, -1.732050808, 1.732050808}`